1. Field of the Invention
The present invention relates to a thread cutting method and a thread cutting cycle generating apparatus. More particularly, the present invention pertains to a thread cutting method which achieves reduction in wear of a tool and in the time required for the process in a so-called thread cutting cycle, as well as a high thread cutting accuracy, and a processing program generating apparatus for generating a thread cutting cycle which employs such a thread cutting method.
2. Description of the Prior Art
In a conventional processing program generating apparatus or a numeral control apparatus (hereinafter simply referred to as "an apparatus") for generating a thread cutting cycle, an intermediate tool path is automatically determined and a thread cutting cycle is thereby generated only by giving commands shown in FIG. 1, including the finished form such as a height of crest of thread H, a cutting depth D from the crest of thread in a first thread cutting operation, and an infeed U at the bottom of thread.
If the cutting depth from the crest of thread in each cutting operation in the thread cutting cycle is d, the cutting depth from the crest of thread in the first cutting operation is d.sub.1, the cutting depth is in the second cutting operation d.sub.2, and the cutting depth in the Nth cutting operation is d.sub.N, and if the infeed in each cutting operation in the thread cutting cycle is .DELTA.d, the infeed in the first cutting operation is .DELTA.d.sub.1, the infeed in the second cutting operation is .DELTA.d.sub.2, and the infeed in the Nth cutting operation is .DELTA.d.sub.N, EQU d.sub.1 =.DELTA.d.sub.1, d.sub.2 =d.sub.1 +.DELTA.d.sub.2, d.sub.N =d.sub.N-1 +.DELTA.d.sub.N ( 1)
The conventional thread cutting method is roughly classified into the equal depth cutting method in which thread cutting is performed on the basis of the relationship expressed by .DELTA.d.sub.1 =.DELTA.d.sub.2 = . . . .DELTA.d.sub.N, and the gradually decreasing depth cutting method in which thread cutting is performed on the basis of the relationship expressed by .DELTA.d.sub.1 &gt;.DELTA.d.sub.2 &gt; . . . .DELTA.d.sub.N. This gradually decreasing depth cutting method is in turn divided into the thread cutting method (hereinafter referred to as "the first thread cutting method") in which the cutting amount in each cutting operation is maintained essentially constant, i.e., in which, if the cutting depth from the crest of thread in the first cutting operation is d.sub.1, the cutting depth from the crest of thread in the second cutting operation is d.sub.2, and the cutting depth from the crest of thread in the Nth cutting operation is d.sub.N, the thread cutting is conducted on the basis of the relation expressed by ##EQU1## and the thread cutting method (hereinafter referred to as "the second thread cutting method") in which the infeed .DELTA.d in each cutting operation is maintained at a predetermined value or above and is reduced to the predetermined value when the number of thread cutting operations are increased (see, for example, Japanese Patent Publication No. 39250/1984).
In order to achieve a reduction in the time required for the thread cutting based on the thread cutting cycle, a cutting amount which is cut out in each thread cutting operation must be made as large as possible. However, the cutting amount in each thread cutting operation cannot be increased to a predetermined value or above due to the cutting conditions (hereinafter referred to as "prerequisites"), including the shape and material of a workpiece, the shape and material of a tool, a cutting resistance, a thread cutting accuracy and wear of the tool. If this predetermined value is an allowable cutting amount S.sub.p, the allowable cutting amount S.sub.p and the length l of a cutting edge used in each thread cutting operation have the following relationship (l.sub.1 in FIG. 1 indicates the length of the cutting edge employed for the first thread cutting operation), EQU S.sub.p =a.sub.1 '.multidot.l+b.sub.1 ( 3)
or, practically, EQU S.sub.p =a.sub.2 '.multidot.l.sup.2 +b.sub.2 ( 4)
where a.sub.1 ', a.sub.2 ', b.sub.1 and b.sub.2 are constants. In a normal thread cutting process, a.sub.1 ' or a.sub.2 ' in the equations (3) and (4) is often a positive value because of the prerequisites and the conditions, including rotation of a spindle and feeding speed (hereinafter referred to as "processing conditions"), and the equations (3) and (4) indicate that the allowable cutting amount S.sub.p increases in proportion to the length l of the cutting edge or the square root of the length l of the cutting edge. In a case where chatter occurs during the process, a.sub.1 ' or a.sub.2 ' in the equations (3) and (4) is a negative value. However, the equations (3) and (4) are effective, as in the former case, and indicate that the allowable cutting amount S.sub.p decreases in proportion to the length l of the cutting edge or the square root of the length l of the cutting edge.
As will be seen from the foregoing description, reduction in the time required for the thread cutting process based on the thread cutting cycle can be achieved if a thread cutting method, in which the cutting amount S can be a value which is less than and closest to the allowable cutting amount S.sub.p, given by the equation (3) or (4), is adopted. However, it is impossible in the conventional thread cutting methods for the cutting amount S to be a value which is less than and closest to the allowable cutting amount S.sub.p for the following reasons:
That is, in the equation (3) or (4), since the length l of the cutting edge and the cutting depth d from the crest of thread in each thread cutting operation in the thread cutting process have the following relationship: EQU l=k d (k: constant, k&gt;0) (5)
if a.sub.1 =a.sub.1 'k, and a.sub.2 =a.sub.2 'k.sub.2, we can reexpress equations (6) and (7) EQU S.sub.p =a.sub.1 d+b.sub.1 ( 6) EQU S.sub.p =a.sub.2 d.sup.2 +b.sub.2 ( 7)
FIG. 2 is a graph in which the abscissa axis represents the cutting depth d while the ordinate axis represents the cutting amount S. In FIG. 2, a straight line p-q represents the relationship between the allowable cutting amount S.sub.p and the cutting depth d, expressed by the equation (6). In that case, the allowable cutting amount S.sub.p =f(d), where f(d)=a.sub.1 d+b.sub.1. The letter H represents the height of crest of thread. A straight line r-t indicates how the cutting amount, expressed by S=g(d), changes in the equal depth cutting method as the cutting depth d changes from D.sub.1, the cutting depth in the first thread cutting operation, to H. The cutting depth D.sub.1 in the first thread cutting operation is determined such that the cutting amount, g(H), obtained when the cutting depth d is equal to H does not exceed the allowable cutting amount S.sub.p (S.sub.p =f(H) obtained when the cutting depth d is equal to H, and the thus obtained value is given as a command. A straight line u-w indicates how the cutting amount, expressed by S=h(d), changes in the first thread cutting method as the cutting depth d changes from D.sub.2, the cutting depth in the first thread cutting operation, to H. The cutting depth D.sub.2 in the first thread cutting operation is determined such that the cutting amount, h(D.sub.2), obtained when the cutting depth d is equal to D.sub.2 is equal to the allowable cutting amount S.sub.p (S.sub.p =f(D.sub.2)) obtained when the cutting depth d is equal to D.sub.2, and the thus obtained value is given as a command. A straight line u-v-t indicates how the cutting amount changes in the second thread cutting method as the cutting depth d changes from D.sub.2, the cutting depth in the first thread cutting operation, to H. The cutting depth D.sub.2 in the first thread cutting operation is determined in the same manner as in the first thread cutting method. Also, the portion u-v represents the portion of the cycle in which the infeed .DELTA.d is not reduced to a fixed value, as in the first thread cutting method, and the portion v-t represents the portion of the cycle in which the infeed .DELTA.d is reduced to a fixed value, as in the depth cutting method.
As stated earlier, in order to achieve a reduction in the time required for thread cutting process based on the thread cutting cycle, the cutting amount must be a value which is less than and closest to the allowable cutting amount S.sub.p, given by the equation (3) or (4), i.e., the equation (6) or (7). That is, a thread cutting method, in which the cutting amount S takes a form which is closest to that represented by the straight line p-q shown in FIG. 2, must be adopted. However, in either the equal depth cutting method represented by the straight line r-t, the first thread cutting method represented by the straight line u-w, and the second thread cutting method represented by the straight line u-v-t, it is impossible for the cutting amount to have a form which is closest to that represented by the straight line p-q.